Point B is the center of the circle shown, and the length of arc AC is 8π. What is the area of the circle?

Question

asked Sep 19, 2021 122k views

2 Answers

Drew Hunter · Answer 1 · 2021-09-26T06:53:16+0000

Answer:

$A=324\pi \text{ units}^2\approx1017.88\text{ units}^2$

Explanation:

The formula for arc length is:

$\stackrel{\frown}{A}=2\pi r((\theta)/(360)})$

Where Θ is measured in degrees.

We know that the arc length is 8π when the degree is 80. So, substitute 8π for A and 80 for Θ:

$8\pi=2\pi r((80)/(360))$

Divide both sides by 2π:

4=r(80)/(360)

Simplify the fraction:

4=(2)/(9)r

Multiply both sides by 9/2:

r=18

So, the radius is 18.

Now, we can find the area of the circle. The formula for the area of a circle is:

$A=\pi r^2$

Substitute 18 into r:

$A=\pi (18)^2$

Simplify:

$A=324\pi \text{ units}^2\approx1017.88\text{ units}^2$

And we're done!